What is the equation of a parabola with (−1, −3) as its focus and y = 1 as its directrix? enter the equation in the box.

The answer

the general formula showing parabola is 
y = ax² + bx +c, its standard form is   y = a(x-h)²  + k
the focus formula is
F(h, k + 1 /4a) and the directrix is
the directrix is V( k - 1/4a) 

so he equation of a parabola with (−1, −3)  as its focus implies
(h, k + 1 /4a) = (−1, −3) 
h =-1, and  k + 1 /4a = -3 
the directrix is  k - 1/4a =1

we should solve the system of equation

k + 1 /4a = -3 
k - 1/4a =1

2k= -3+1 = -2, so k =-1 and when we use this value 

-1 -1/4a = 1 implies 2 = -1/4a  this equation give a = -1/8

finally the equation is 

y = -1/8 (x +1)² -1